few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

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options: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Use probability to evaluate outcomes of decisions.

Investigate chance processes and develop, use, and evaluate probability models.

Develop understanding of statistical variability.

Use random sampling to draw inferences about a population.

Interpret linear models.

Summarize and describe distributions.

Understand and evaluate random processes underlying statistical experiments.

Understand independence and conditional probability and use them to interpret data.

Calculate expected values and use them to solve problems.

Draw informal comparative inferences about two populations.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Summarize, represent, and interpret data on a single count or measurement variable.

Investigate patterns of association in bivariate data.
problem_activity: Activity
In this activity, students continue to develop their understanding of what could be considered typical for a group as well as variability in a data set. Students compare distributions with the same mean but different spreads and interpret them in the context of a situation. The context given here (basketball score) prompts them to connect the mean to the notion of how “well” a player plays in general, and deviations from the mean to how “consistently” that player plays.
They encounter the idea of calculating the
average absolute deviation from the mean
as a way to describe variability in data.
Launch
Arrange students in groups of 3–4. Give groups 6–7 minutes to answer the questions and follow with a whole-class discussion.
Action and Expression: Internalize Executive Functions.
Begin with a small-group or whole-class demonstration and think aloud to remind students how calculate mean using data from a dot plot.  Keep the worked-out calculations on display for students to reference as they work.
Supports accessibility for: Memory; Conceptual processing
Listening, Speaking: MLR2 Collect and Display.
Use this routine to collect student ideas and language about playing “well” and “consistently” as they discuss the players’ data in the three dot plots. Record students’ language on a display for all to see. This will help students connect their reasoning about the visual representations of data to statistical terms such as mean, deviation from the mean, and variability in data.
Design Principle(s): Support sense-making
Student Facing
Here are the dot plots showing the number of baskets Elena, Jada, and Lin each made over 12 school days.
On each dot plot, mark the location of the mean with a triangle (
\(\Delta\)
). Then, contrast the dot plot distributions. Write 2–3 sentences to describe the shape and spread of each distribution.
[IMG]
Discuss the following questions with your group. Explain your reasoning.
Would you say that all three students play equally well?
Would you say that all three students play equally consistently?
If you could choose one player to be on your basketball team based on their records, who would you choose?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
The purpose of the discussion is to highlight that the center of the distribution is not always the only consideration when discussing data. The variability or spread can also influence how we understand the data.
There are many ways to answer the second set of questions. Invite students or groups who have different interpretations of “playing well” and “playing consistently” to share their thinking. Allow as many interpretations to be shared as time permits. Discuss:
“How might we use the given data to quantify ‘playing well’ and ‘playing consistently?’”
“Is there a way to describe variability and consistency in playing precisely and in an objective way (rather than using broad, verbal descriptions)?”
Explain that we can describe variability more formally and precisely—using a number to sum it up; we will look at how to do so in the next activity.


correct_option_index: 4

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